Birmingham city council is in trouble. It's financial situation, already precarious, worsened last year after 170 former employees won an equal pay claim, leaving the council with a huge staffing bill to settle.

Now Birmingham leader Sir Albert Bore has sent an open letter to the government warning that its financial position is even worse than he had first feared. Cuts to government grant now leave the authority needing to find savings of £825m by 2018 – a step too far for the council to take.

"The upshot is that the true reduction in core government grants in 2015-16 will actually be 14.5%, rather than 10%, and we estimate that this will result in yet another worsening of around £23m a year in the funding gap," Bore stated.

Bore used the letter to call on the National Audit Office (NAO) to examine the way central government has managed the control of funding to councils, assessing whether the future of local government is viable at all under current funding restrictions.

This is unlikely to happen given that the NAO published an analysis of the sustainability of local government earlier this year – which did indeed find unique pressures on councils thanks to the decisions of Whitehall.

What is most interesting about Bore's letter, however, is the language he uses in describing the position of his authority.

"To pretend that [savings] can be delivered by traditional efficiencies and the sort of savings the secretary of state for communities and local government has highlighted is simply misleading," he writes. "This council has not sought to delude itself or its citizens that these massive budget reductions can be achieved in this way."

Indeed. Chancellor George Osborne and communities secretary Eric Pickles – he who takes the ministerial role of critical friend very literally – do not want councils to plug the gaps with "traditional efficiencies". And Pickles knows he doesn't have the answers himself. He wants councils to behave like entrepreneurs and find innovative ways to overcome the hurdles that he is laying out in front of them. He wants to see what has become known as "transformation".

The problem is that local authorities and their services are rarely staffed by innovators and entrepreneurs. Transformation isn't happening because leaders often can't imagine what the end result might look like – and where they can, they don't always like what they see.

The New Local Government Network thinktank runs a series of training events with local councils called Anyborough that allows politicians and officers to take tough restructuring and budgeting decisions on behalf of a fictional authority. The fascinating thing about this exercise is how rarely the teams taking part come up with genuinely transformational ideas until the only other option is, for example, to axe social care services altogether.

So, when Bore talks about being unable to find savings in the usual manner, there's no doubt he's right. But what could Birmingham do if it learns to think differently? To stop thinking like local government?

I'm no apologist for Pickles and Osborne. I understand that the heart is being stripped out of communities as boxes are ticked in Whitehall by people far removed from the real impact of the decisions they make.

But now it is out there's little chance of putting the genie back, so it is up to councils to learn to think differently. They must take advice from entrepreneurs and innovators on how to rescue public services. They must accept that while the old way worked very well and should have been protected the responsibility of finding a new and sustainable future is now on their shoulders. There is no backing out.